Helly Theorems and Generalized Linear Programming

@inproceedings{Amenta1993HellyTA,
  title={Helly Theorems and Generalized Linear Programming},
  author={Nina Amenta},
  booktitle={Symposium on Computational Geometry},
  year={1993}
}
Recent combinatorial algorithms for linear programming also solve certain non-linear problems. We call these Generalized Linear Programming, or GLP, problems. One way in which convexity has been generalized by mathematicians is through a collection of results called the Helly theorems. We show that the every GLP problem implies a Helly theorem, and we give two paradigms for constructing a GLP problem from a Helly theorem. We give many applications, including linear expected time algorithms for… CONTINUE READING

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